A Note on Sparse Supersaturation and Extremal Results for Linear Homogeneous Systems

Christoph Spiegel
2017 Electronic Journal of Combinatorics  
We study the thresholds for the property of containing a solution to a linear homogeneous system in random sets. We expand a previous sparse Szémeredi-type result of Schacht to the broadest class of matrices possible. We also provide a shorter proof of a sparse Rado result of Friedgut, Rödl, Ruciński and Schacht based on a hypergraph container approach due to Nenadov and Steger. Lastly we further extend these results to include some solutions with repeated entries using a notion of non-trivial
more » ... ion of non-trivial solutions due to Rúzsa as well as Rué et al.
doi:10.37236/6730 fatcat:jltdjrofqvhcrbisix7jyrz6h4